Abstract

Ehrhart theory is the theory studying how many lattice points are contained in the dilate of a given (lattice) polytope; it has rich applications to combinatorial problems, and deep connections to algebraic geometry, representation theory and more. Some of the most fundamental problems remain open.

We developed a new approach to understanding the fundamental class of associated semigroup algebras via Parseval-Rayleigh identities. This leads to the resolution of several combinatorial conjectures, such as unimodality of the $h^\ast$-polynomial for large classes of lattice polytopes, among them integrally closed Gorenstein polytopes.

Based on joint work with Papadakis and Petrotou. If time permits, I will also give glimpses of upcoming work that involves in addition Katz and Oba.

Biography

Karim Alexander Adiprasito is a Directeur de Recherche Exceptionelle at the Jussieu Institute of Mathematics - Paris Rive Gauche (IMJ-PRG), Sorbonne Université. His research interests are in Combinatorics and metric geometry. 
He was born 1988 in Germany. He had studied at TU Dortmund (2007-2010), the Institute of Mathematics @ IIT Bombay (2008-2009) and FU Berlin (2010-2013), where he was awarded the Ernst Reuter prize of the Free University for his thesis. 
After being an EPDI fellow at IHES, a Minerva fellow at Hebrew University and a member at the Institute for Advanced Study, he joined the faculty of the Hebrew University in 2015 (tenured 2016) and since 2019 in Copenhagen.
In 2016, he won a grant by the European Research Council (ERC) and the Israel Science foundation (ISF), which support his research projects. In addition, he was awarded the European Prize in Combinatorics in 2015, the Klachky prize of the Hebrew University in 2017, was named a Knut & Alice Wallenberg fellow (at KTH) in 2018, and was awarded the 2019 New Horizons Prize in Mathematics. Since 2022/23, he is at CNRS.